{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "825734f6",
   "metadata": {},
   "source": [
    "# SuStaIn tutorial -- October 2021\n",
    "\n",
    "![SuStaIn](https://media.springernature.com/full/springer-static/image/art%3A10.1038%2Fs41467-018-05892-0/MediaObjects/41467_2018_5892_Fig1_HTML.png?as=webp)\n",
    "Image from [Young et al. Nat Comms 2018](https://doi.org/10.1038/s41467-018-05892-0)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07b69425",
   "metadata": {},
   "source": [
    "In the present tutorial, we will go through the process of running SuStaIn, from data preprocessing to evaluating output, on a simulated dataset. The code below can serve as a code-base for your own SuStaIn analyses,\n",
    "\n",
    "Note that we are using the Z-score SuStaIn for this demonstration, but versions of SuStaIn exist for binary and ordinal data as well."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86788114",
   "metadata": {},
   "source": [
    "## Installing SuStaIn and setting it up to run in a notebook\n",
    "\n",
    "To get SuStaIn up and running first you need to install the package. I'm using Anaconda and had some conflicts with existing packagaes so I had to create a new environment. For me the whole set up process looked like this...\n",
    "\n",
    "Step 1: Open up a terminal window and create a new environment \"sustain_env\" in anaconda that uses python 3.7 and activate the environment ready to install pySuStaIn.\n",
    "```console\n",
    "conda create --name sustain_tutorial_env python=3.7\n",
    "conda activate sustain_tutorial_env\n",
    "```\n",
    "\n",
    "Step 2: Use the terminal to install necessary packages for running the notebook and pySuStaIn within the environment.\n",
    "```console\n",
    "conda install -y ipython jupyter matplotlib statsmodels numpy pandas scipy seaborn pip\n",
    "pip install git+https://github.com/ucl-pond/pySuStaIn\n",
    "```\n",
    "\n",
    "Step 3: Use the terminal to run the notebook from inside the environment.\n",
    "```console\n",
    "jupyter notebook\n",
    "```\n",
    "\n",
    "Once you've got your environment running the general workflow will be to open a terminal window and navigate to the directory with the notebook in, activate the envirnoment, open a jupyter notebook inside and use the notebook to run your analyses, then use the terminal deactivate the environment once you've finished running analyses.\n",
    "```console\n",
    "conda activate sustain_tutorial_env\n",
    "jupyter notebook\n",
    "conda deactivate\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e8a4431f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load libraries\n",
    "\n",
    "import os\n",
    "import pandas\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pySuStaIn\n",
    "import statsmodels.formula.api as smf\n",
    "from scipy import stats\n",
    "import sklearn.model_selection\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "42981e5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load and view simulated tutorial data\n",
    "# The data needs to be in the same directory as your notebook\n",
    "\n",
    "data = pandas.read_csv('SimulatedData.csv')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "278a25e2",
   "metadata": {},
   "source": [
    "It seems was have both patients (Diagnosis = 1) and controls (Diagnosis = 0) in this dataset. Let's quickly look how many we have of each"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3a96bdb8",
   "metadata": {},
   "outputs": [],
   "source": [
    "data.Diagnosis.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "76dd2794",
   "metadata": {},
   "outputs": [],
   "source": [
    "# store our biomarker labels as a variable\n",
    "biomarkers = data.columns[4:]\n",
    "print(biomarkers)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84e63dbe",
   "metadata": {},
   "source": [
    "# Normalize to control group\n",
    "\n",
    "SuStaIn expects z-score cutoffs for each variable as input. Right now, our data is \"raw\" data. We want to convert this data to Z-scores, and it would be great to use the \"Control\" population as the reference for this z-score normalization. That way, we can interpret a Z score of 1 to mean 1 SD from the mean of a control population.\n",
    "\n",
    "In this case, our biomarkers are \"raw\" values (let's pretend they are brain volumes\"), and we also wany to adjust them for confounding effects of Age and Headsize.\n",
    "\n",
    "The following section will convert our biomarkers into age- and headsize- adjusted Z scores, using the control subjects as a reference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "02eba419",
   "metadata": {},
   "outputs": [],
   "source": [
    "# first a quick look at the patient and control distribution for one of our biomarkers\n",
    "\n",
    "biomarker = biomarkers[0]\n",
    "sns.displot(data=data, # our dataframe\n",
    "            x=biomarker, # name of the the distribution we want to plot\n",
    "            hue='Diagnosis', # the \"grouping\" variable\n",
    "            kind='kde') # kind can also be 'hist' or 'ecdf'\n",
    "plt.title(biomarker)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3cd82da9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# now we perform the normalization\n",
    "\n",
    "# make a copy of our dataframe (we don't want to overwrite our original data)\n",
    "zdata = pandas.DataFrame(data,copy=True)\n",
    "\n",
    "# for each biomarker\n",
    "for biomarker in biomarkers:\n",
    "    mod = smf.ols('%s ~ Age + Headsize'%biomarker,  # fit a model finding the effect of age and headsize on biomarker\n",
    "                  data=data[data.Diagnosis==0] # fit this model *only* to individuals in the control group\n",
    "                 ).fit() # fit model    \n",
    "    #print(mod.summary())\n",
    "    \n",
    "    # get the \"predicted\" values for all subjects based on the control model parameters\n",
    "    predicted = mod.predict(data[['Age','Headsize',biomarker]]) \n",
    "    \n",
    "    # calculate our zscore: observed - predicted / SD of the control group residuals\n",
    "    w_score = (data.loc[:,biomarker] - predicted) / mod.resid.std()\n",
    "    \n",
    "    #print(np.mean(w_score[data.Diagnosis==0]))\n",
    "    #print(np.std(w_score[data.Diagnosis==0]))\n",
    "    \n",
    "    # save zscore back into our new (copied) dataframe\n",
    "    zdata.loc[:,biomarker] = w_score\n",
    "    \n",
    "    \n",
    "plt.figure(0)\n",
    "sns.scatterplot(x=data.Age,y=data.Biomarker1,hue=data.Diagnosis)\n",
    "plt.figure(1)\n",
    "sns.scatterplot(x=zdata.Age,y=zdata.Biomarker1,hue=zdata.Diagnosis)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09797d93",
   "metadata": {},
   "source": [
    "Now that we've normalized the data, let's look at the new distribution and make sure it looks right"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce0138c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "biomarker = biomarkers[0]\n",
    "sns.displot(data=zdata,x=biomarker,hue='Diagnosis',kind='kde')\n",
    "plt.title(biomarker)\n",
    "plt.axvline(0,ls='--',c='black') # the 0 line *should* be the mean of the control distribution\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa2a8a32",
   "metadata": {},
   "source": [
    "# Prepare SuStaIn inputs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df05bb98",
   "metadata": {},
   "source": [
    "Now that we've z-scored our data, let's start prepping the many SuStaIn inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f2d80c48",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = len(biomarkers)         # number of biomarkers\n",
    "\n",
    "SuStaInLabels = biomarkers\n",
    "Z_vals = np.array([[1,2,3]]*N)     # Z-scores for each biomarker\n",
    "Z_max  = np.array([5]*N)           # maximum z-score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e960a489",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(Z_vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "48653367",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Input the settings for z-score SuStaIn\n",
    "# To make the tutorial run faster I've set \n",
    "# N_startpoints = 10 and N_iterations_MCMC = int(1e4)\n",
    "# I recommend using N_startpoints = 25 and \n",
    "# N_iterations_MCMC = int(1e5) or int(1e6) in general though\n",
    "\n",
    "N_startpoints = 10\n",
    "N_S_max = 3\n",
    "N_iterations_MCMC = int(1e4)\n",
    "output_folder = os.path.join(os.getcwd(), 'WorkshopOutput')\n",
    "dataset_name = 'WorkshopOutput'\n",
    "\n",
    "# Initiate the SuStaIn object\n",
    "sustain_input = pySuStaIn.ZscoreSustain(\n",
    "                              zdata[biomarkers].values,\n",
    "                              Z_vals,\n",
    "                              Z_max,\n",
    "                              SuStaInLabels,\n",
    "                              N_startpoints,\n",
    "                              N_S_max, \n",
    "                              N_iterations_MCMC, \n",
    "                              output_folder, \n",
    "                              dataset_name, \n",
    "                              False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28dc4a46",
   "metadata": {},
   "source": [
    "# Run SuStaIn!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "92f5252e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# make the output directory if it's not already created\n",
    "if not os.path.isdir(output_folder):\n",
    "    os.mkdir(output_folder)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "99704057",
   "metadata": {},
   "outputs": [],
   "source": [
    "samples_sequence,   \\\n",
    "samples_f,          \\\n",
    "ml_subtype,         \\\n",
    "prob_ml_subtype,    \\\n",
    "ml_stage,           \\\n",
    "prob_ml_stage,      \\\n",
    "prob_subtype_stage  = sustain_input.run_sustain_algorithm()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4ae6043",
   "metadata": {},
   "source": [
    "# Evaluate subtypes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4593c9a1",
   "metadata": {},
   "source": [
    "Here, we'll plot the log likelihood across MCMC samples, across each subtype. This will give us at least a basic sense of what how many subtypes we should consider looking at"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "294a2df7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# for each subtype model\n",
    "for s in range(N_S_max):\n",
    "    # load pickle file (SuStaIn output) and get the sample log likelihood values\n",
    "    pickle_filename_s = output_folder + '/pickle_files/' + dataset_name + '_subtype' + str(s) + '.pickle'\n",
    "    pk = pandas.read_pickle(pickle_filename_s)\n",
    "    samples_likelihood = pk[\"samples_likelihood\"]\n",
    "    \n",
    "    # plot the values as a line plot\n",
    "    plt.figure(0)\n",
    "    plt.plot(range(N_iterations_MCMC), samples_likelihood, label=\"subtype\" + str(s))\n",
    "    plt.legend(loc='upper right')\n",
    "    plt.xlabel('MCMC samples')\n",
    "    plt.ylabel('Log likelihood')\n",
    "    plt.title('MCMC trace')\n",
    "    \n",
    "    # plot the values as a histogramp plot\n",
    "    plt.figure(1)\n",
    "    plt.hist(samples_likelihood, label=\"subtype\" + str(s))\n",
    "    plt.legend(loc='upper right')\n",
    "    plt.xlabel('Log likelihood')  \n",
    "    plt.ylabel('Number of samples')  \n",
    "    plt.title('Histograms of model likelihood')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f918758",
   "metadata": {},
   "source": [
    "It is very clear from this output that two subtypes fits the data better than one subtype, but adding a third subtype does not improve the model fit significantly. Let's move forward with the 2 subtype model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9550f636",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's plot positional variance diagrams to interpret the subtype progressions\n",
    "\n",
    "s = 1 # 1 split = 2 subtypes\n",
    "M = len(zdata) \n",
    "\n",
    "# get the sample sequences and f\n",
    "pickle_filename_s = output_folder + '/pickle_files/' + dataset_name + '_subtype' + str(s) + '.pickle'\n",
    "pk = pandas.read_pickle(pickle_filename_s)\n",
    "samples_sequence = pk[\"samples_sequence\"]\n",
    "samples_f = pk[\"samples_f\"]\n",
    "\n",
    "# use this information to plot the positional variance diagrams\n",
    "tmp=pySuStaIn.ZscoreSustain._plot_sustain_model(sustain_input,samples_sequence,samples_f,M,subtype_order=(0,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "947b72fd",
   "metadata": {},
   "source": [
    "It seems we have one subtype where Biomarker 3 becomes severe quickly, and a second where Biomarker 3 becomes abnormal far later, while Biomarker 5 occurs earlier."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a5bc343",
   "metadata": {},
   "source": [
    "# Subtype and stage individuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "21096bf6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's take a look at all of the things that exist in SuStaIn's output (pickle) file\n",
    "pk.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3f97ab64",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "# The SuStaIn output has everything we need. We'll use it to populate our dataframe.\n",
    "\n",
    "s = 1\n",
    "pickle_filename_s = output_folder + '/pickle_files/' + dataset_name + '_subtype' + str(s) + '.pickle'\n",
    "pk = pandas.read_pickle(pickle_filename_s)\n",
    "\n",
    "for variable in ['ml_subtype', # the assigned subtype\n",
    "                 'prob_ml_subtype', # the probability of the assigned subtype\n",
    "                 'ml_stage', # the assigned stage \n",
    "                 'prob_ml_stage',]: # the probability of the assigned stage\n",
    "    \n",
    "    # add SuStaIn output to dataframe\n",
    "    zdata.loc[:,variable] = pk[variable] \n",
    "\n",
    "# let's also add the probability for each subject of being each subtype\n",
    "for i in range(s):\n",
    "    zdata.loc[:,'prob_S%s'%i] = pk['prob_subtype'][:,i]\n",
    "zdata.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0d423219",
   "metadata": {},
   "outputs": [],
   "source": [
    "# IMPORTANT!!! The last thing we need to do is to set all \"Stage 0\" subtypes to their own subtype\n",
    "# We'll set current subtype (0 and 1) to 1 and 0, and we'll call \"Stage 0\" individuals subtype 0.\n",
    "\n",
    "# make current subtypes (0 and 1) 1 and 2 instead\n",
    "zdata.loc[:,'ml_subtype'] = zdata.ml_subtype.values + 1\n",
    "\n",
    "# convert \"Stage 0\" subjects to subtype 0\n",
    "zdata.loc[zdata.ml_stage==0,'ml_subtype'] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ef6b84ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "zdata.ml_subtype.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aad38760",
   "metadata": {},
   "source": [
    "As a sanity check, let's make sure all the \"controls\" were given assigned to low stages by SuStaIn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "edcda23a",
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.displot(x='ml_stage',hue='Diagnosis',data=zdata,col='ml_subtype')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9528ad0",
   "metadata": {},
   "source": [
    "And now, let's plot the subtype probabilities over SuStaIn stages to make sure we don't have any crossover events"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "824df7ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.pointplot(x='ml_stage',y='prob_ml_subtype', # input variables\n",
    "              hue='ml_subtype',                 # \"grouping\" variable\n",
    "            data=zdata[zdata.ml_subtype>0]) # only plot for Subtypes 1 and 2 (not 0)\n",
    "plt.ylim(0,1) \n",
    "plt.axhline(0.5,ls='--',color='k') # plot a line representing change (0.5 in the case of 2 subtypes)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d500ef79",
   "metadata": {},
   "source": [
    "# Evaluate relationships"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d12c733",
   "metadata": {},
   "source": [
    "One might want to view whether there are relationships between SuStaIn subtype and stage and other variables.\n",
    "\n",
    "This step should probably be done after you run cross-validation (see below), but we'll do it here first to keep up the momentum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "09601f9f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plotting relationship between a biomarker and SuStaIn stage across subtypes\n",
    "\n",
    "var = 'Biomarker3'\n",
    "\n",
    "# plot relationship\n",
    "sns.lmplot(x='ml_stage',y=var,hue='ml_subtype',\n",
    "          data = zdata[zdata.ml_subtype>0],\n",
    "           #lowess=True # uncomment if you would prefer a lowess curve to a linear curve\n",
    "          )\n",
    "\n",
    "# get stats\n",
    "for subtype in [1,2]:\n",
    "    # get r and p value\n",
    "    r,p = stats.pearsonr(x = zdata.loc[zdata.ml_subtype==subtype,var].values,\n",
    "                         y = zdata.loc[zdata.ml_subtype==subtype,'ml_stage'].values)\n",
    "    # add them to plot\n",
    "    plt.text(16,0-subtype,'S%s: r = %s, p = %s'%(subtype,round(r,3),round(p,2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5e64b2a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# we can also look at differences in each biomarker across subtypes\n",
    "\n",
    "from scipy import stats\n",
    "results = pandas.DataFrame(index=biomarkers)\n",
    "for biomarker in biomarkers:\n",
    "    t,p = stats.ttest_ind(zdata.loc[zdata.ml_subtype==0,biomarker],\n",
    "                         zdata.loc[zdata.ml_subtype==1,biomarker],)\n",
    "    results.loc[biomarker,'t'] = t\n",
    "    results.loc[biomarker,'p'] = p\n",
    "    \n",
    "print(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "45e987dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.heatmap(pandas.DataFrame(results['t']),square=True,annot=True,\n",
    "           cmap='RdBu_r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "44ce59bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot an example variable:\n",
    "\n",
    "var = 'Biomarker3'\n",
    "sns.boxplot(x='ml_subtype',y=var,data=zdata)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa1aa09f",
   "metadata": {},
   "source": [
    "# Cross-validation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40e79cdf",
   "metadata": {},
   "source": [
    "Finally, it is often difficult to decide how many subtypes best fit your data. This question should ideally be evaluated using cross-validation. This way, the likelihood metrics are generated for data that the model has not yet seen. \n",
    "\n",
    "FYI we may not have nough time to run this full cross-validation during the workshop, but it's good for you to run it yourself. SuStaIn also support parallelized cross-validation!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9372159f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# choose the number of folds - here i've used three for speed but i recommend 10 typically\n",
    "N_folds = 3\n",
    "\n",
    "# generate stratified cross-validation training and test set splits\n",
    "labels = zdata.Diagnosis.values\n",
    "cv = sklearn.model_selection.StratifiedKFold(n_splits=N_folds, shuffle=True)\n",
    "cv_it = cv.split(zdata, labels)\n",
    "\n",
    "# SuStaIn currently accepts ragged arrays, which will raise problems in the future.\n",
    "# We'll have to update this in the future, but this will have to do for now\n",
    "test_idxs = []\n",
    "for train, test in cv_it:\n",
    "    test_idxs.append(test)\n",
    "test_idxs = np.array(test_idxs,dtype='object')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7169f8d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# perform cross-validation and output the cross-validation information criterion and\n",
    "# log-likelihood on the test set for each subtypes model and fold combination\n",
    "CVIC, loglike_matrix     = sustain_input.cross_validate_sustain_model(test_idxs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c47faee9",
   "metadata": {},
   "source": [
    "# Choosing the optimal number of subtypes\n",
    "The optimal number of subtypes is chosen using the CVIC, shown below. The CVIC is an information criterion (like the AIC/BIC/WAIC) that balances model complexity with model accuracy, with a lower CVIC indicating a better balance between the two. Generally speaking, the model with the lowest CVIC is the best. However, you do sometimes get a very small improvement (less than ~6) in the CVIC with a more complex model, in which case I would tend to favour the less complex (i.e. fewer subtypes) model.\n",
    "\n",
    "Another useful metric to look at is the log-likelihood of each subtypes model on the test set, also shown below. A better model should show a consistent improvement in the test set log-likelihood across folds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a212adcb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# go through each subtypes model and plot the log-likelihood on the test set and the CVIC\n",
    "print(\"CVIC for each subtype model: \" + str(CVIC))\n",
    "print(\"Average test set log-likelihood for each subtype model: \" + str(np.mean(loglike_matrix, 0)))\n",
    "\n",
    "plt.figure(0)    \n",
    "plt.plot(np.arange(N_S_max,dtype=int),CVIC)\n",
    "plt.xticks(np.arange(N_S_max,dtype=int))\n",
    "plt.ylabel('CVIC')  \n",
    "plt.xlabel('Subtypes model') \n",
    "plt.title('CVIC')\n",
    "\n",
    "plt.figure(1)\n",
    "df_loglike = pandas.DataFrame(data = loglike_matrix, columns = [\"s_\" + str(i) for i in range(sustain_input.N_S_max)])\n",
    "df_loglike.boxplot(grid=False)\n",
    "plt.ylabel('Log likelihood')  \n",
    "plt.xlabel('Subtypes model') \n",
    "plt.title('Test set log-likelihood across folds')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae8d5b9b",
   "metadata": {},
   "source": [
    "Another useful output of the cross-validation that you can look at are positional variance diagrams averaged across cross-validation folds. These give you an idea of the variability in the progression patterns across different training datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d2a6d957",
   "metadata": {},
   "outputs": [],
   "source": [
    "#this part estimates cross-validated positional variance diagrams\n",
    "for i in range(N_S_max):\n",
    "    sustain_input.combine_cross_validated_sequences(i+1, N_folds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "badef262",
   "metadata": {},
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    "N_S_selected = 2\n",
    "\n",
    "pySuStaIn.ZscoreSustain._plot_sustain_model(sustain_input,samples_sequence,samples_f,M,subtype_order=(0,1))\n",
    "_ = plt.suptitle('SuStaIn output')\n",
    "\n",
    "sustain_input.combine_cross_validated_sequences(N_S_selected, N_folds)\n",
    "_ = plt.suptitle('Cross-validated SuStaIn output')"
   ]
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